Problem: Simplify the following expression: $p = \dfrac{-10z - 12}{10z + 14}$ You can assume $z \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-10z - 12 = - (2\cdot5 \cdot z) - (2\cdot2\cdot3)$ The denominator can be factored: $10z + 14 = (2\cdot5 \cdot z) + (2\cdot7)$ The greatest common factor of all the terms is $2$ Factoring out $2$ gives us: $p = \dfrac{(2)(-5z - 6)}{(2)(5z + 7)}$ Dividing both the numerator and denominator by $2$ gives: $p = \dfrac{-5z - 6}{5z + 7}$